Canary, I changed the colour of the grout on our bathroom floor tiles with Flysea grout tile pens. I was really pleased with the result. Takes a while but quite easy to get a good and neat finish.
It may depend on what you are changing from to. I changed a dark mucky brown to grey.
I've acquired some pens and the results are looking good (it's only a small toilet floor Zebu, and the result justifies the means. It's a good job duck-herding is in the Close Season, so I can spare the time.)
Glad the pens worked fine, Canary. I planned to use them as a temporary fix til we had a new floor. So pleased with the result that three years on the floor is still the same and the grout colour lasting well.